Electromigration

September 12, 2011

As I've found in the transition from bulky, vacuum tubeelectronics, such as televisions, radios and sound systems, to the lightweight and compact units sold today, going small has many benefits. Unfortunately, these benefits didn't come until after my nomad days when it seemed that I was moving my household on an annual basis.

When these current-carrying conductor traces are thin in both thickness and width, the cross-sectional area of these conductors become very small. At a given current, the current density becomes extremely large. Although we don't really associate electrical current with movement, current is the movement of electrons, and these electrons do run into some resistance in the conductors. Otherwise, we would have a superconductor, and not the mundane aluminum, copper or gold in our integrated circuits.

The Faraday constant is the magnitude of electric charge of one mole of electrons. The unit of electrical current, the ampere, is the flow of 6.241 x 1018 electrons (a coulomb) per second, or a little more than 1 x 10-5 Faradays per second.

An electron in a conductor, when it meets resistance in the metallattice, imparts a momentum against the resistance, effectively pushing atoms out of the way. The effect is very small on a per electron basis, but at high current densities, things start to add up. Gaps will actually open in thin conductors as enough atoms are pushed out of the way by electrons.

Fortunately, materials scientists know a few tricks, one of which is that the addition of small amounts of copper to aluminum, which mechanically hardens it, increases its current handling capacity by many times. There's no free lunch, so copper addition does reduce the conductivity of aluminum. Electromigration doesn't happen in semiconductors, but a heavily-doped semiconductor behaves like a metal, and these are susceptible to electromigration.

There has been much interest in using carbon nanotubes in integrated electronics, so the question naturally arises as to what electromigration effects might be seen in carbon nanotube circuitry. That's what a team from the US National Institute of Standards and Technology (NIST) investigated, and they discovered some reliability issues that are partially explained by electromigration.[1-3]

The NIST team fabricated circuits in which carbon nanotube arrays connected gaps in metal electrodes. They found that the nanotubes are good current carriers that sustain extremely high current densities. The supported current densities were one- to two-orders of magnitude greater that those found in a typical integrated circuit. These current densities were supported for several hours, but they slowly degraded. The initial current densities were as high as ten mega-ampere per square centimeter![3]

Those currents must pass also through the metalization, also, and that demonstrated another problem. The metal electrodes failed. The edges of the metalization receded and clumped, as shown in the micrograph below. The combined carbon-nanotube-metal conductors failed after times up to about 40 hours.[1]

Micrograph of recession and clumping in gold electrodes after application of 1.7 volts to the carbon nanotubes for an hour.

The NIST data also showed a way to predict which circuits would fail early, and which would continue conducting current for a longer period. The NIST team found that the initial resistance was a predictor of total device lifetime.[3] Their electron microscopy studies indicated that variability in the fabrication of the circuits was an important factor in the rate of degradation. Well-fabricated conductors under constant current conditions showed a linear accumulation of damage reminiscent of electromigration. Oxygen and waterdesorption are suspected to be further contributing factors in degradation, but this mechanism could not be confirmed.[3]

While I was in graduate school, I worked alongside a team that investigated electromigration in the exotic materials, ZrPt3 and HfPt3.[4] These alloys are highly stable intermetallic compounds. ZrPt3, has an enthalpy of formation (ΔHf) of -124 kcal/mole and a melting point of about 2400 K (3850 °F). HfPt3 has an enthalpy of formation (ΔHf) of -132 kcal/mole and the same melting point.[5] These metals have tightly-bonded atoms that would not be expected to easily migrate. I wrote about these alloys in a previous article (Krell metal, August 31, 2006).